Upper critical limit

It has been established (P8, R5) that when the value of S exceeds about 0.25, the liquid bridges begin to coalesce with one another and the bonding mechanism changes over from the pendular to the funicular state. When S exceeds 0.8, the existence of discrete liquid bridges is no longer possible and now the capillary pressure state alone exists. Thus, the funicular state lies in a range of saturation bounded by the lower and upper critical limits denoted by Sp and Sc, respectively. 

To summarize Figure 18-1 in words, the top curve represents the characteristics of a population P0 with mean /x0. Also indicated in Figure 18-1 is the upper critical limit, marking the 95% point for a standard hypothesis test (//0) that the mean of a given sample is consistent with /x . A measured value above the critical value indicates that it would be too unlikely to have come from population P0, so we would conclude that such a reading came from a different population. Two such possible different, or alternate, populations are also shown in Figure 18-1, and labeled Pt and P2. Now, if in fact a random sample was taken from one of these alternate populations, there is a given probability, whose value depends on which population it came from, that it would fall above (or below) the upper critical limit indicated for H0. 

Comprehensive studies of the oscillatory features of B-Z reaction involving double substrate such as (i) glucose -F acetone (ii) fructose -F acetone and (iii) sucrose -F acetone have been made. One of the interesting features is that the systems display the lower and upper critical limits of [acetone] between which oscillations occurred on increasing [F]. Another significant observation was that beyond a certain [F], oscillations occurred even when no acetone was present in the system. Obviously, at this stage Br -control mechanism is not in operation [46] and an alternative free-radical control... 

The assumption in step 1 would first he tested hy obtaining a random sample. Under the assumption that p <. 02, the distrihiition for a sample proportion would he defined hy the z distrihiition. This distrihiition would define an upper hound corresponding to the upper critical value for the sample proportion. It would he unlikely that the sample proportion would rise above that value if, in fact, p <. 02. If the observed sample proportion exceeds that limit, corresponding to what would he a very unlikely chance outcome, this would lead one to question the assumption that p <. 02. That is, one would conclude that the null hypothesis is false. To test, set... 

As indicated above, when a positive direct current is impressed upon a piece of titanium immersed in an electrolyte, the consequent rise in potential induces the formation of a protective surface film, which is resistant to passage of any further appreciable quantity of current into the electrolyte. The upper potential limit that can be attained without breakdown of the surface film will depend upon the nature of the electrolyte. Thus, in strong sulphuric acid the metal/oxide system will sustain voltages of between 80 and 100 V before a spark-type dielectric rupture ensues, while in sodium chloride solutions or in sea water film rupture takes place when the voltage across the oxide film reaches a value of about 12 to 14 V. Above the critical voltage, anodic dissolution takes place at weak spots in the surface film and appreciable current passes into the electrolyte, presumably by an initial mechanism involving the formation of soluble titanium ions. 

UOP FCC unit, 11 700-702 UOP/HYDRO MTO process, 18 568 UOP Olex olefin separation process, 17 724 Up-and-Down Method, 25 217 U/Pb decay schemes, 25 393-394 Updraft sintering, 26 565 Upflow anaerobic sludge blanket (UASB) in biological waste treatment, 25 902 Upgraded slag (UGS), 25 12, 33 Upland Cotton, U.S., 8 13 U-Polymer, 20 189 Upper critical solution temperature (UCST), 20 320, 322 Upper explosive limit (UEL), 22 840 Upper flammability limit, 23 115 Upper flammable limit (UFL), 22 840 Upper Freeport (MVB) coal... 

Hc2- k-(ET)2Cu(NCS)2 gave higher upper critical magnetic field H 2 values in the two-dimensional plane than the Pauli limited magnetic field //pauii [226, 227]. 

Bubble-size control was also critical. The intensity of scattering by nonresonant gas bubbles is proportional to the sixth power of the radius of the bubble. Hence, the larger the bubble, the better the scattering intensity. However, the acceptable upper size limit for in vivo administration is determined by the need for bubbles to cross capillary beds. Bubbles larger than 6-8 pm should be avoided as they are trapped in the lung capillaries. The current accepted sizes are in 1-7 pm, preferably around 3 pm, with as narrow a size distribution as possible. Bubble shell material needs to be biodegradable. Soft shells are generally preferable, as they minimally impede US backscatter. 

The critical value of CVp has to be lower than the maximum permissible true value (e.g. lower than CVp 0.128 when there is no bias). The maximum permissible value of the true CVp will be referred to as its "target level". In order to have a confidence level of 95% that a subject method meets this required target level, on the basis of CVp estimated from laboratory tests, an upper confidence limit for CVp is calculated which must satisfy the following criterion reject the method (i.e. decide it does not meet the accuracy standard) if the 95% upper confidence limit for CVp exceeds the target level of CVp. Otherwise, accept the method. This decision criterion was implemented in the form of the Decision Rule given below which is based on assumptions that errors are normally distributed and the method is unbiased. Biased methods are discussed further below. 

For our validations, a CVp is a pooled estimate calculated from the particular type of statistical data set (36 samples) described earlier in the Statistical Experimental Design section of this report. A statistical procedure is given in Hald JL for determining an upper confidence limit for the coefficient of variation. This general theory had o be adapted appropriately for application to a pooled CVp estimate. For this design, and under the stated assumptions, there is a one-to-one correspondence between values of CVp and upper confidence limits for CVp. Therefore, the confidence limit criterion given above is equivalent to another criterion based on the relationship of CVp and its critical value. The... 

In cases where confidence limits can be calculated for the bias, the critical CV-p should be read from the dotted curve at a position corresponding to the 95% upper confidence limit for the bias. This is a conservative procedure. 

The constancy of the critical AT agrees with the equation-of-state explanation of superheated liquids and with the reaction-rate view of nucleation. It means there is an upper temperature limit above which a superheated liquid cannot exist (at a stated pressure) regardless of agitation. 

Interactions between different distant parts of the molecule tend to expand it, so that in the absence of other effects a would be greater than unity, but in solution in poor solvents interactions with the solvent tend to contract it. According to Flory s theory (18) these two tendencies will just balance so that a — 1 at a particular temperature T—0 (the theta temperature ), and at this temperature A2 =0 and further this temperature is the limit as Mn- go of the upper critical solution temperature for the polymer-solvent system in question. Quantities relating to T=0 will be denoted by subscript 0. Flory s theory implies that ... 

Fig. 20. (a) Temperature dependence of the upper critical field calculated within a two-band model for several impurity scattering rates yjmp (cm-1). (b) calculated Hc2(0)-vi.-ylmp curve illustrating the transition from the clean to the dirty limit. Dotted line Hc2(0)-y,mp dependence in the dirty limit. (Drechsler et al. 2000 Fuchs... 

Fig. 60. Concentration dependence of various properties of polycrystalline Y(Ni xPt )2B2C obtained by specific heat measurements transition temperature Tc exponent a and parameter Hc2 from eq. (6) upper critical field Hc2(0) at T =0, where the dotted line schematically describes the dirty limit corresponding to the isotropic single band case (in reality there is a finite intersection with the field-axis for the dotted asymptotic line, see Shulga and Drechsler 2002) exponent fi of eq. (8) for the curvature of the electronic specific heat in the mixed state and Sommerfeld constant xn (after Lipp et al. 2001).

The critical limit may be an upper limit or a lower limit. This comes about in the following way. Chains are interrupted either by deactivation at the wall or in the gas phase. The greater the concentration of the gases, the smaller relatively is the influence of the wall factor. When this is the chief means by which the chains are broken there may be a transition from slow reaction to explosion as the pressure increases. When, on the other hand,... 

The S-L-V curve intersects the gas-liquid critical curve in two points the lower critical end point (LCEP) and the upper critical end point (UCEP). At these two points, the liquid and gas phases merge into a single fluid-phase in the presence of excess solid. At temperatures between Tlcep and Tucep a S-V equilibrium is observed. The solubility of the heavy component in the gas phase increases very rapidly with pressure near the LCEP and the UCEP. Near the LCEP the solubility of heavy component in the light one is limited by the low temperatures. In contrast, near the UCEP the solubility of heavy component in the light one is high, owing to the much higher temperatures [6],... 

Studies on non-ionic surfactants as effective drag-reducing additives have been submitted by Zakin (1972). He studied various effects on three non-ionic surfactants formed from straight-chain alcohols and ethyleneoxide. These surfactants have an upper and a lower temperature limit for solubility in water and prove effective drag reducers near their upper critical solubility temperature or clouding point. The clouding point is the point at which a solution of a non-ionic agent in water becomes turbid as the temperature is raised. 

As can be seen from the phase diagram in Figure 4.6, which has been redrawn to be consistent with our results between 1373 and 1973 K (1100-1700°C), the j3-V2N phase indeed attains the composition of 33.3 mol%N as expected from structural considerations. This upper compositional limit is based on data from several independently investigated diffusion couples at four different temperatures (mean value 33.35 0.30 mol%N). It is considerably different from the generally accepted literature values where in a critical evaluation18 a value of 31 mol%N was given preference over a value of 32.8 mol%N by Brauer and Schnell.19... 

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